The present invention relates to screening systems in general and, more particularly, to a second order Moire free screening system and method.
Offset printing is a binary process: the press can print INK or NO INK on a particular location of the paper. Unlike in the photographic or other "contone" reproduction processes, no controlled modulation of the ink density is possible to obtain the various shades of tone and color.
To simulate the effect of different densities, necessary for the reproduction of pictures, patterns of dots are used of which the SIZE is modulated. 0% dot size corresponds with no ink, while 100% dot size corresponds with a solid ink area. The process of simulating densities by modulating dot sizes is called "halftoning".
The patterns of dots are defined by an angle (measured along the direction of the shortest line that connects two dot centers, a screen ruling (defined by the number of dot centers per measurement unit, measured in the direction of the screen angle), and the shape of the dots as they grow from 0% to 100% (usually controlled by a "spot function").
In conventional color printing, four inks are used: cyan, magenta, yellow and black. Every printable color is simulated by overprinting a particular combination of dot percentages of these four inks.
The angles and rulings of the dot patterns of these four inks are chosen with the following two considerations in mind:
1) In order to reduce the sensitivity of the color reproduction to registration errors, the relative position of the dots of the four inks has to be (pseudo) randomized. 2) It is known that geometrical patterns of dots interact with each other, and can give raise to new patterns that are referred to as "Moire". The dot patterns in color printing should be chosen not to give raise to disturbing Moire patterns.
In conventional technology, both of these two requirements are achieved by using dot patterns for the cyan, magenta and black inks that have exactly the same ruling, and by using angles that are exactly 30 and 60 degrees offset with respect to each other. The yellow ink is usually printed with a screen using the same ruling as the others, and an angle that is 15 degrees offset with respect to one of the other inks. A combination of angles that works well is:
cyan: 75.0 degrees PA0 black: 45.0 degrees PA0 magenta: 15.0 degrees PA0 yellow: 0.0 degrees PA0 alfa=arctan(A/B); PA0 freq=res/sqrt(A*A+B*B); PA0 res: resolution. PA0 alfa=arctan(A/B); PA0 freq=m*res/sqrt(A*A+B*B); PA0 res: resolution. PA0 m: multiplicity. PA0 M.sub.-- x=F1*cos(alfa1)+F2*cos(90.0-alfa2)-F3*cos(alfa3); PA0 M.sub.-- y=F1*sin(alfa1)-F2*sin(90.0-alfa2)-F3*sin(alfa3); PA0 M.sub.-- period=1.0/sqrt(M.sub.-- x*M.sub.-- x+M.sub.-- y*M.sub.-- y); PA0 Given: A,B,res. PA0 res=2400 dpi, A=4, B=15. PA0 By applying the formulas: PA0 alfa1=14.9314 degrees; F1=154.5976 PA0 alfa2=45.0000 degrees; F2=154.2778 PA0 alfa3=75.0686 degrees; F3=154.5976 PA0 endpoint screen1: (x0,y0)=(F1*cos(alfa1), F1*sin(alfa1)) PA0 endpoint screen3: (x1,y1)) =(F3*cos(alfa3), F3*sin(alfa3)) PA0 or, because: F1=F3, cos(alfa3)=sin(alfa1), sin(alfa3)=cos(alfa1): PA0 endpoint screen1: (x0,y0)=(F1*cos(alfa1), F1*sin(alfa1)) PA0 endpoint screen3: (x1,y1)=(F1*sin(alfa1), F1*cos(alfa1)) PA0 3*z*z*z*z-16*z*z*z+22*z*z-16*z+4=0 PA0 with: z=A/B; PA0 z0=2.0-sqrt(3.0); PA0 z1=2.0+sqrt(3.0); PA0 Given: PA0 res=2400; A=15; B=56; m=3; PA0 sceen1: alfa1=14.9951; F1=124.1933; PA0 sceen1: alfa2=45.0000; F2=124.1748; PA0 sceen3: alfa3=75.0049; F3=F1;
It can be shown that if exactly these angles are used, the same relative position of the cyan, magenta and black dots is never repeated, which meets the first requirement, while the "Moire" is a "micro Moire" (often referred to as the "rosette"), which, when screen rulings are used of approximately 150 l/i, is small enough not to be disturbing.